Anisotropic critical phenomena in parabolic geometries: the directed self-avoiding walk

Abstract

The critical behaviour of directed self-avoiding walks is studied on parabolic-like systems with a free boundary at x=\pm Ct^α. Using a scaling argument, 1/C is shown to be a marginal variable when α=ν_\perp/ν_\parallel=1/2, i.e., on a parabola. As a consequence the directed walk may display varying local exponents. Such a behaviour is indeed observed for restricted walks. This generalizes a result of Cardy showing that nonuniversal behaviour occurs at corners for isotropic systems.

arXiv commentOld paper, for archiving. 8 pages, 1 figure, epsf, IOP macro

References in corpus (1)

• Critical behaviour in parabolic geometries

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